1. Field of the Invention
The invention relates to a method for measuring the flow parameters of a fluid and to a device utilizing this method. This method and this device are utilized more particularly in the medical field, the fluid in question then being the blood of a patient, and the flow parameters which are of interest are the mean speed of flow of the blood and the distribution of the speeds of the particles of this blood in a particular section of a vein or artery. Its most useful application is ultrasonic echography.
The measurement of the mean speed of a fluid in a tube is of interest since it renders it possible to determine the rate of fluid flow, if the cross-section of the tube in question is known. The distribution of the speeds of the fluid particles in the section of the tube renders it possible to assess the presence or absence of turbulence phenomena in the flow. It will thus be grasped intuitively that a flow undergoing but little disturbance will have a mean speed of flow substantially equal to the speed at all points of a cross-section, whereas a highly disturbed flow displays a great spread in its speed diagram. In a turbulent flow, fluid particles may even be present which are displaced in the opposite direction of that of the mean speed of flow in view of the presence of vortices.
It is known that the speed of flow of an elementary volume or "cell" of a fluid may be measured by transmitting a pulsed acoustic signal oscillating at an acoustic frequency in the direction of this cell by means of a probe. The signal transmitted is propagated as far as the cell, is reflected from the same and disseminated rearwardly in all directions and in particular towards the probe. Once the period of propagation in both directions between the probe and a cell under examination is known however, it is possible to open a time slot for receiving the reflected signal and none other. In practice, the probes utilized are reversible probes of a piezo-electric type, able to perform a periodic transmission at a given recurrence frequency of the pulsed sound signal and arranged for reception of the reflected signal, outside the transmission periods. In view of its reflection on a cell in motion, and by Doppler effect, the signal transmitted back oscillates at a sound frequency differing from the transmission frequency. The shift .DELTA.f between these two frequencies, established by Doppler effect, may be written as: ##EQU1##
In this expression, v and c respectively represent the speed of a particle of the cell reflecting the sound and the speed of sound in the intermediate medium. The value .beta. is the angle subtended between the direction of flow within the tube and the axis of the ultrasonic beam. The value fo is the frequency of the ultrasonic pulse transmitted.
On technological as well as experimental grounds, the useful sizes of the cells cannot be reduced as much as might be wished. In the greater proportion of cases, each of the dimensions of these cells, be it in width, length or depth, is wholly comparable to the dimensions of the flow tube cross-section. As a result, the signal transmitted back does not oscillate at a single sound frequency displaced by Doppler shift from the acoustic transmission frequency, but is a complex signal of which the spectrum distribution extends over a significant band. For example, for a group of particles of a cell flowing at speeds comprised between zero meters/second and four meters/second, the Doppler shift corresponding to each of these particles will be comprised between zero and 25 kilohertz if the acoustic transmission frequency is of the order of 4 megahertz and if the speed of propagation of the acoustic pulse in the interposed medium is of the order of 1500 meters/sec.
In view of the close correspondence between a speed of flow and a Doppler shift, a theory has been formulated for mensuration of the flow parameters of a fluid by measuring the spectral density of the signal transmitted back. If Z(t) denotes the signal transmitted back, the spectral density Z(f) is the modulus taken to the square of the Fourier transformation of the signal Z(t); this may be set down in the following form: EQU Z(f)=.vertline..intg.Z(t).multidot.e.sup.-2.pi.ft .multidot.dt.vertline..sup.2
Until the present invention, it was known that the means speed of flow of the fluid may be measured by calculation of the whole spectum Z(f) to allow calculation of the mean frequency from the same, and to assess the more or less turbulent nature of the flow on the basis of the typical deviation or variance of this spectrum Z(f). The function Z(f) referred to in the continuation of this specification is not actually the spectrum of the signal transmitted back, but the spectrum of the signal transmitted back which had been exposed to an acoustic frequency demodulation and to a low-pass filtering operation so that it then represents none but the spectrum of the Doppler shift as such. It may be demonstrated that these considerations have no bearing on the validity of the preceding expression Z(f).
2. Description of the Prior Art
Based on this theory, those versed in the art seek to calculate as precisely as possible the amplitude of each of the lines of the spectrum of Z(f). To this end, they utilize equipment performing a fast Fourier transformation (referred to as FFT). As a matter of fact, this FFT equipment performs a discrete Fourier transformation of the signal. This means that for each pulse of the signal transmitted back, the signal received is demodulated by means of two oscillators in phase quadrature, each of the two signals thus demodulated is filtered by means of a low-pass filter, and quantified samples are taken by means of blocking samplers followed by analog-digital converters at the end of an always constant period following the onset of the pulse transmission. The FFT equipment thus collects a plurality of successive samples corresponding to a plurality of pulses of the signal received. After a period of calculation, they provide a set of numeric values representing the amplitudes of each of the lines of spectrum.
This FFT equipment has a first disadvantage which is related to its calculation circuits. As a matter of fact, this may operate on a number of samples only, which is a power of 2: for example 64 or 128 samples. Much as it may be appreciated that the accuracy of the results given by this method increases with the number of samples, it is no less understandable that this method implies assumptions regarding the constancy of the flow action under investigation. If the flow is not constant, it is appropriate to consider the same steady flow for a limited period only, implying a limitation of the number of samples to be taken into account for a given measurement precision. If, allowing for constancy, the optimum sample number is of the order of 90, it is observed that mensuration by means of FFT equipment has disadvantages since 90 is not a power of 2.
If the moments of order n of the Fourier transformation are denoted by m.sub.n, it is possible to state: EQU m.sub.n =.intg.f.sup.n .multidot.Z(f).multidot.df
The result is that m.sub.o is equal to the energy of the signal returned, m.sub.1 corresponds to the mean frequency, and that the variance .sigma. sought has the form: EQU .sigma..sup.2 =m.sub.2 -m.sub.1.sup.2
On the basis of standardization, it is acceptable to represent the means speed by m.sub.1 /m.sub.o and the variance by: ##EQU2##
Notwithstanding the fact that each of these terms m.sub.o, m.sub.1 and m.sub.2 must be calculated, which is onerous, the method yields results of which the accuracy largely depends on the signal/noise ratio of the signal returned. In practice, the signal/noise ratio of the signal returned should be at least 20 dB. Now, the walls of the flow tube give rise to the appearance of fixed echoes, situated around zero hertz in Doppler shift since the walls vibrate a little under the action of the flow. These fixed echoes are commonly much more powerful than the useful signal: their amplitude exceeds that of the latter by a magnitude of the order of 30 dB. The elimination of the fixed echoes consequently requires the presence of echo-rejector filters of costly construction since the flanks of these filters should be very rigid to enable them to reject the echoes at approximately 30 dB below the value of the useful signal. Their rejection ratio should actually exceed or be equal to 20 dB+30 dB=50 dB.
Furthermore, it is necessary to make allowance for the noises of quantification, apart from mensuration noises. As a matter of fact, because of allowing for a value close to the demodulated quantities, these introduce an additional error into the calculation results. If N is the spectral noise density within the band of the useful signal, it is necessary to replace Z(f) by Z(f)-N;
N can be calculated easily by measuring its value in the absence of a returned signal. It is very onerous on the contrary to introduce N into the calculation of each of the moments of the Fourier transformation of Z(t).
Another method which does not make use of FFT equipment yields a diagram of the spectrum of the useful return signal by counting, for each of the pulses, the passages through zero of the filtered demodulated return signal. For a counting period known beforehand, the number of passages through zero of the filtered demodulated signal is directly proportional to the mean frequency of this signal during the pulse in question. It is appropriate however to observe that the result given by this method for the mean frequency is not a precise result in the first place and is highly affected by noise in the second place. The result is not precise since it may be shown that it is proportional to: ##EQU3## which is not strictly equal to m.sub.1 /m.sub.o which is the true value. The method for counting the passages through zero is impervious to noise moreover since, to prevent accidental counting actions in the presence of noise, the counters incorporate a pair of lower and upper thresholds and a counting action is caused only if these two different thresholds are traversed successively by the signal. As a result, the measurement of the mean frequency is always obtained in a deficient manner, since no allowance is made for the oscillations of the filtered demodulated return signal of which the amplitudes are comprised between these two thresholds. On the other hand, the more the signal is affected by noise, the more it is appropriate to raise the thresholds and the greater the inaccuracy of the result.